Problem: Ben is 2 times as old as Nadia. Twelve years ago, Ben was 8 times as old as Nadia. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Nadia. Let Ben's current age be $b$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $b = 2n$ Twelve years ago, Ben was $b - 12$ years old, and Nadia was $n - 12$ years old. The information in the second sentence can be expressed in the following equation: $b - 12 = 8(n - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $n$ and substitute it into our second equation. Solving our first equation for $n$ , we get: $n = b / 2$ . Substituting this into our second equation, we get: $b - 12 = 8($ $(b / 2)$ $- 12)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 12 = 4 b - 96$ Solving for $b$ , we get: $3 b = 84$ $b = \dfrac{1}{3} \cdot 84 = 28$.